Quartic double solids with ordinary singularities

TL;DR

This paper investigates the mixed Hodge structure and Torelli problem for specific threefolds that are double covers of projective three-space ramified over a quartic surface with a double conic, revealing new insights into their geometric properties.

Contribution

It provides a detailed analysis of the mixed Hodge structure and addresses the Torelli problem for quartic double solids with ordinary singularities, a novel focus in algebraic geometry.

Findings

Characterization of the mixed Hodge structure on the third homology group.

Results on the Torelli problem for these threefolds.

Insights into the geometry of double covers ramified over quartic surfaces with singularities.

Abstract

We study the mixed Hodge structure on the third homology group of a threefold which is the double cover of projective three-space ramified over a quartic surface with a double conic. We deal with the Torelli problem for such threefolds.